A note on vectorial AdS5/CFT4 duality for spin-j boundary theory

A bstract The vectorial holographic correspondences between higher-spin theories in AdS 5 and free vector models on the boundary are extended to the cases where the latter is described by free massless spin- j field. The dual higher-spin theory in the bulk does not include gravity and can only be defined on rigid AdS 5 background with S 4 boundary. We discuss various properties of these rather special higher-spin theories and calculate their one-loop free energies. We show that the result is proportional to the same quantity for spin- j doubleton treated as if it is a AdS 5 field. Finally, we consider even more special case where the boundary theory itself is given by an infinite tower of massless higher-spin fields.